Properties

Label 380.2.v
Level $380$
Weight $2$
Character orbit 380.v
Rep. character $\chi_{380}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
Newform subspaces $3$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

Total New Old
Modular forms 256 256 0
Cusp forms 224 224 0
Eisenstein series 32 32 0

Trace form

\( 224q - 2q^{2} - 4q^{5} - 20q^{8} + O(q^{10}) \) \( 224q - 2q^{2} - 4q^{5} - 20q^{8} - 2q^{10} + 4q^{12} - 4q^{13} - 4q^{17} - 64q^{20} - 8q^{21} + 22q^{22} - 4q^{25} + 16q^{26} - 16q^{28} + 12q^{30} - 12q^{32} + 8q^{33} - 68q^{36} - 16q^{37} - 30q^{38} + 8q^{40} - 16q^{41} + 30q^{42} - 56q^{45} + 24q^{46} - 28q^{48} + 12q^{50} - 18q^{52} - 4q^{53} - 16q^{56} - 12q^{57} - 140q^{58} + 14q^{60} - 72q^{61} + 12q^{62} - 48q^{65} - 12q^{66} + 4q^{68} - 82q^{70} + 56q^{72} - 4q^{73} + 60q^{76} + 48q^{77} + 48q^{78} - 2q^{80} + 40q^{81} + 16q^{82} + 20q^{85} + 64q^{86} + 104q^{88} - 92q^{90} + 4q^{92} - 24q^{93} - 32q^{96} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
380.2.v.a \(4\) \(3.034\) \(\Q(\zeta_{12})\) None \(-4\) \(6\) \(-2\) \(0\) \(q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
380.2.v.b \(4\) \(3.034\) \(\Q(\zeta_{12})\) None \(2\) \(-6\) \(-2\) \(0\) \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+\zeta_{12}+\cdots)q^{3}+\cdots\)
380.2.v.c \(216\) \(3.034\) None \(0\) \(0\) \(0\) \(0\)